You are preparing to enter a competition against $n$ opponents, indexed from $0$ to $n - 1$. You are given two integers initialEnergy and initialExperience, along with two integer arrays energy and experience, both of length $n$.

To defeat opponent i, your current energy must be strictly greater than energy[i], and your current experience must be strictly greater than experience[i].

When you defeat opponent i:

• Your energy decreases by energy[i].

• Your experience increases by experience[i].

Before starting the competition, you can train for any integer number of hours. In one hour of training, you can choose to increase either your energy by $1$ or your experience by $1$.

Return the minimum total number of training hours needed to defeat all $n$ opponents in sequence from index $0$ to $n - 1$.

Constraints:

• n $==$ energy.length $==$ experience.length

• $1 \le$ n $\le 100$

• $1 \le$ initialEnergy, initialExperience, energy[i], experience[i] $\le 100$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.